In Chapter XV. we find the greatest number of errors. Take, for
example, the following computation of the diminution of gravity at
the surface of the sun in consequence of the centrifugal force,--part
of the data being, that a pound at the earth's surface will weigh
twenty-eight pounds at the sun's surface, and that the centrifugal
force at the earth's equator is 1/289 of gravity.
"Now, if the sun rotated in the same time as the earth, and their
diameters were equal, the centrifugal force on the equators of the
two orbs would be equal. But the sun's radius is about 111 times that
of the earth, and if the period of rotation were the same, the
centrifugal force at the sun's equator would be greater than that at
the earth's in the ratio of (111)^2 to 1, or, more exactly, in the
ratio of 12,342.27 to 1. But the sun rotates on its axis much slower
than the earth, requiring more than 25 days for one revolution. This
will reduce the above in the ratio of 1 to (25)^2, or 1 to 625; so
that we shall have the earth's equatorial centrifugal force (1/289) x
12,342.27 / 625 = 12,342.27/180,605 = 0.07 nearly for the sun's
equatorial centrifugal force. Hence the weight before obtained, 28
pounds, must be reduced seven hundredths of its whole value, and we
thus obtain 28 - 0.
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